Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime

Abstract

In this paper, we study the Cauchy and Goursat problems of the spin-$n/2$ zero rest-mass equations on Minkowski spacetime by using the conformal geometric method. In our strategy, we prove the wellposedness of the Cauchy problem in Einstein's cylinder. Then we establish pointwise decays of the fields and prove the energy equalities of the conformal fields between the null conformal boundaries $\scri^\pm$ and the hypersurface ${\Sigma }_0=\left\{t=0\right\}$. Finally, we prove the wellposedness of the Goursat problem in the partial conformal compactification by using the energy equalities and the generalisation of Hörmander's result.

42 pages, 3 figures

References in corpus (5)

• Sharp decay estimates for massless Dirac fields on a Schwarzschild background
• Conformal Scattering and the Goursat Problem for Dirac Fields in the Interior of Charged Spherically Symmetric Black Holes
• Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field
• Peeling of Dirac fields on Kerr spacetimes
• Conformal scattering theory for the linearized gravity fields on Schwarzschild spacetime

Cited by in corpus (1)

• Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime